### Thue equations and the method of Coleman-Chabauty, by Dino Lorenzini and Thomas J. Tucker

In this paper, we prove that a Thue equation F(x,y) = h, where h is
an integer and F is a polynomial of degree n with integer coefficients and
without repeated roots, has at most 2n^3 - 2n - 3 solutions provided that
the Mordell-Weil rank of the Jacboian of the corresponding curve is less than
(n-1)(n-2)/2. The proof uses the method of Coleman-Chabauty, extended here to
apply to arbitrary regular models of curves, along with an explicit
construction of a portion of a regular model for the curve corresponding to
the Thue equation.

Dino Lorenzini and Thomas J. Tucker <lorenz@math.uga.edu, ttucker@math.uga.edu>